Since colleges aren’t designed in order to fit categories, the categories are descriptive rather than prescriptive. Since that’s the case, there are grey areas, schools that could go either way (Dartmouth is an oft-cited example, as is Wesleyan). I think of Deep Springs as an LAC because I think it has nothing meaningful in common with community colleges, but feel free to differ. There’s no conclusive answer, though–this is heuristic taxonomizing, not algorithmic.